Simplify the following expression: $ k = \dfrac{3}{7} + \dfrac{1}{a - 6} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{a - 6}{a - 6}$ $ \dfrac{3}{7} \times \dfrac{a - 6}{a - 6} = \dfrac{3a - 18}{7a - 42} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{1}{a - 6} \times \dfrac{7}{7} = \dfrac{7}{7a - 42} $ Therefore $ k = \dfrac{3a - 18}{7a - 42} + \dfrac{7}{7a - 42} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{3a - 18 + 7}{7a - 42} $ $k = \dfrac{3a - 11}{7a - 42}$